Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau 3-folds

Abstract

We solve Bershadsky–Cecotti–Ooguri–Vafa (BCOV) holomorphic anomaly equation to determine the higher genus Gromov–Witten invariants ($g\geq 5$) of the derived equivalent Calabi–Yau 3-folds, which are of the appropriate codimensions in the Grassmannian Gr(2, 7) and the Pfaffian Pf(7).Let $q\geq n-p$